Abstract: For the communication system with uplink and downlink bidirectional transmission task in the actual scene, this paper proposes a two-way relay cooperative non-orthogonal multiple access (NOMA) transmission scheme, which studies the uplink and downlink two-way transmission of signals based on decode and forward (DF) protocol. This scheme allocates more power to the near user which different from the existing NOMA schemes, and realizes bidirectional information exchange between base station and users by network coding(NC) principle. Further considering the imperfect channel state information (CSI) condition, the transmission performance of the system is analyzed, and the expressions of outage probability, ergodic sum rate are derived. Simulation results show that, compared with the scheme proposed in the existing literature , one-way relay（OWR）and orthogonal multiple access (OMA) networks, the proposed scheme can effectively reduce the transmission outage probability, improve the traversal rate and throughput of the system under perfect CSI and imperfect CSI conditions.